Zusammenfassung

For a strongly elliptic second-order operator A on a bounded domain Rn it has been known for many years how to interpret the general closed L2()-realizations of A
as representing boundary conditions (generally nonlocal), when the domain and coeffcients are smooth. The purpose of the present paper is to extend this representation to
nonsmooth domains and coeffcients, including the case of ...

Zusammenfassung

For a strongly elliptic second-order operator A on a bounded domain Rn it has been known for many years how to interpret the general closed L2()-realizations of A
as representing boundary conditions (generally nonlocal), when the domain and coeffcients are smooth. The purpose of the present paper is to extend this representation to
nonsmooth domains and coeffcients, including the case of Hölder C 3/2+"-smoothness, in such a way that pseudodifferential methods are still available for resolvent constructions and ellipticity considerations. We show how it can be done for domains with B 3/2 2;p-smoothness and operators with H1 q -coeffcients, for suitable p > 2(n